What is ((y-8)^2)/4-((x-5)^2)/9 =1 ?

The solution to ((y-8)^2)/4-((x-5)^2)/9 =1 is Hyperbola with (h,k)=(5,8),a=2,b=3

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((y-8)^2)/4-((x-5)^2)/9 =1

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

(h, k) = (5, 8), a = 2, b = 3

Solution steps

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

Rewrite

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

in the form of a standard hyperbola equation

\frac{( y - 8 ) ^{2}}{2 ^{2}} - \frac{( x - 5 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, 8), a = 2, b = 3

4 x^{2} - y^{2} - 4 y - 40 = 0

x^{2} - y^{2} + 4 x - 6 y = 6

x^{2} - 4 y^{2} - 8 x + 16 y - 36 = 0

2 = x^{2} - y^{2}

- 5 x^{2} + 4 y^{2} = 16

What is ((y-8)^2)/4-((x-5)^2)/9 =1 ?
The solution to ((y-8)^2)/4-((x-5)^2)/9 =1 is Hyperbola with (h,k)=(5,8),a=2,b=3